## Linear Operators: Spectral theory |

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Page 860

A B -

in a B -

= x * + y * , ( xy ) * = y * * * ( x ) * = āx * , ( w * ) * = x . All of the examples ...

A B -

**algebra**X is commutative in case xy = yæ for all x and y in X . An involutionin a B -

**algebra**X is a mapping x → * * of X into itself with the properties ( x + y ) *= x * + y * , ( xy ) * = y * * * ( x ) * = āx * , ( w * ) * = x . All of the examples ...

Page 868

Nelson Dunford, Jacob T. Schwartz. 2 . Commutative B - Algebras In case X is a

commutative B -

is again a commutative

Nelson Dunford, Jacob T. Schwartz. 2 . Commutative B - Algebras In case X is a

commutative B -

**algebra**every ideal I is two - sided and the quotient**algebra**X / Iis again a commutative

**algebra**. It will be a B -**algebra**if I is closed ( 1 . 13 ) .Page 979

be based upon two closely related commutative algebras of operators in the

Hilbert space Ly ( R ) . One of these algebras , namely the

preceding section , we have met before . For convenience , its definition and

some of its ...

be based upon two closely related commutative algebras of operators in the

Hilbert space Ly ( R ) . One of these algebras , namely the

**algebra**A of thepreceding section , we have met before . For convenience , its definition and

some of its ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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